Performance analysis of the BDSBAS-B1C message in trial operation stage

BeiDou Satellite-based Augmentation System (BDSBAS) has come into the trial operation stage since July, 2020. To evaluate the characteristic of the augmentation message in BDSBAS-B1C signal, the effectiveness of the message content was firstly analyzed, and then the validity of the broadcasting strategy was estimated. Finally, the accuracy of the user equivalent ranging error (UERE) and the single frequency positioning error with different correction parameters in BDSBAS-B1C message was evaluated. Based on the above analysis, the effectiveness of the augmentation message was preliminarily verified with the results showing that: (1) the BDSBAS-B1C message type, information content and update interval have basically met the international standard; (2) the accuracy of the UERE obtained with the augmentation message had an obvious improvement in contrast to that of the UERE obtained with the usual navigation message of the GPS satellites, and the ionospheric delay was one of the important factors which affected the accuracy of the UERE; (3) the positioning accuracy obtained with the augmentation message was also improved, and the improvement was more obvious in the service areas with high availability of the ionospheric parameters.


BDSBAS overview
BDSBAS is an important part of the BDS-3, mainly applied in civil aviation, maritime and railway. As shown in Fig. 1, the BDSBAS mainly consists of three parts: the space segment, the ground segment and the user segment.
Space segment of the BDSBAS. The space segment consists of three BDS GEO satellites. As showed in The augmented satellites will include BDS-3 medium orbit earth (MEO), inclined geosynchronous orbit (IGSO) satellites and other GNSS satellites, such as global position system (GPS), Galileo satellite navigation system (Galileo) and global navigation satellite system (GLONASS) satellites. At present, the augmentation message of the GPS satellites is broadcasted in BDSBAS-B1C signal and BDSBAS-B2a signal, while the augmentation message for BDS-3 satellites is only broadcasted in BDSBAS-B2a signal.
Ground segment of the BDSBAS. The ground segment of the BDSBAS is constructed with the BDS-3 ground segment, including monitoring stations, data processing centers, main control stations and injection stations. The distribution of the stations has not been published.
The space-time reference system maintained by the BDSBAS SF service keeps consistent with WAAS. The coordinate system of BDSBAS is WGS-84. The deviation of BDSBAS SF service network time (SNT) to GPS Time (GPST) is within 50 ns.
User segment of the BDSBAS. The civil terminal of the BDSBAS mainly includes the airborne terminal and land terminal. The airborne terminals can be applied in commercial aviation, general aviation and unmanned aerial vehicles. The land-based terminals can be used for the low dynamic land-based or maritime equipment.

Broadcasting status of the BDSBAS-B1C message
The current SBASs are independent and regional operating systems, which mainly provide augmentation service to civil aviation users within the coverage area of their respective systems 3 . How to realize the seamless connection in the overlapping area has become an inevitable issue for the performance improvement of the SBAS services 6 . The consistency of the signal system and message structure is the basic requirement.  Figure 1. Illustration of the BDSBAS architecture. It consists of three parts: a space segment, which includes GEO satellites and other global navigation satellite system (GNSS) satellites; a ground segment, which includes monitoring stations, data processing centers, master stations and uplink stations; a user segment, which mainly includes the civil aviation users. www.nature.com/scientificreports/ The realization of the BDSBAS-B1C message is depend on the BDS signal-in-space interface control document: satellite based augmentation system service signal BDSBAS-B1C, which strictly follows the Satellite Based Augmentation System (SBAS) Standards and Recommended Practices (SARPs) of ICAO "Convention on International Civil Aviation" Annex 10 Aeronautical Telecommunications Volume I Radio Navigation Aids 7 .
Based on the signal characteristics and message structure described in the BDSBAS-B1C document, the message content and broadcasted strategy can be analyzed with the actual message.
Message content of the BDSBAS-B1C. The broadcasted BDSBAS-B1C message mainly includes fast corrections, long-term satellite error corrections, ionospheric corrections and the corresponding integrity parameters. Based on the message broadcasted from Dec 11 to 31, 2020, Table 1 gives the broadcasted message type (MT), information definitions, and content descriptions. The MT0 information was broadcast at least once every 6 s to indicate that the system was still in the testing stage. The other MT represented different kinds of broadcasted message, for example, MT1 symbolizes the message of PRN mask assignment.
Not all messages defined in the BDSBAS-B1C message were broadcasted, such as the offset parameters of BDSBAS SNT and UTC (MT12) and the fast corrections/long term satellite error corrections (MT24). These messages were also not broadcasted regularly in WAAS. Whereas, EGNOS, a system which could augment GPS and GLONASS, provided not only the MT 12 but also the SBAS service message (MT 27). As the augmented object of the BDSBAS was also the GPS and GLONASS, the MT 12 and MT 27 may also be broadcasted in BDSBAS-B1C signal as EGNOS.
The details of the broadcasted messages are further described in the following paragraphs: (1) The correction parameters and the integrity parameters of the 32 GPS satellites have been broadcasted regularly. When the satellites were not in the BDSBAS service area or an alarm event occurs, the correction information of the corresponding satellites should not be broadcasted or set as a default value. Some alarm events have been monitored, which were mainly caused by the low availability as the satellite got close to the service boundary. (2) As shown in Table 2, it could be seen that when the satellites were within the BDSBAS service area, the statistic values of the orbit correction (three-dimensional), clock correction and fast correction parameters were about 1.6 m, 0.48 m and 0.15 m, respectively, and the corresponding UDREI was about 4, meaning that the maximum value of the user differential ranging error (UDRE) was 2.25 m. The broadcasted fast correction and integrity information of the PRN20 satellite was shown in Fig. 3 and the positioning and clock correction information from Dec 11 to 31, 2020 was shown in Fig. 4. Compared with the parameters broadcasted by the adjacent MASAS, the values were basically in the same magnitude.
The positioning and clock correction information on Dec 11, 2020 was shown in Fig. 5. It could be seen that as the satellite came into/out of the service area, the position corrections in different directions were zero while the www.nature.com/scientificreports/ clock correction was not. It can be deduced that the resolving condition of the position corrections was stricter than the clock correction and the resolving of the orbit and clock error was separated.
(3) The ionospheric corrections of the fixed IGPs were shown in Fig. 6 which cannot be guaranteed with 100% availability temporarily, especially the service boundary areas. It can be deduced that the BDSBAS may also adopt the inverse distance weighting algorithm, which was initially adopted by the initial WAAS to calculate the ionospheric delay of the IGPs 8,9 as the low availability of the boundary area. As the development of WAAS, it adopted the Kriging interpolation algorithm to calculate the ionospheric delay, which could greatly reduce the reliance on the monitoring stations and improve the IGPSs availability in the boundary areas 10,11 . While, the applicability of this algorithm for the BDSBAS should be further demonstrated.
Normally, the broadcasted ionospheric grids are fixed. To improve the service performance and ensure the availability of each grid, WAAS has made four major adjustments. Whereas, the availability of the ionospheric grids surrounding the BDSBAS service boundary were rather low. Therefore, BDSBAS may further adjust the ionospheric grids.
(4) MT28 contained an upper triangular E and a scale factor ( SF 1 ). The calculation method is shown in the following formula (1) and (2). Then, the observation covariance matrix C which reflected the clock error δt and the ephemeris errors in three directions ( δx, δy, δz ) could be obtained. The resolving process was shown in formula (3): In the formula, E referred to the clock-ephemeris covariance matrix and E 1,1 to E 1,4 referred to the matrix elements; SF 1 was a scale factor whose value was 2 (scale exponent-5) ; C referred to a relative covariance matrix of R.
Therefore, E 1,4 , E 2,4 and E 3,4 broadcasted in MT28 are the elements concerned with (δx, δt), (δy, δt), (δz, δt) respectively. As the values of the E 1,4 , E 2,4 and E 3,4 parameters are all 0, it could be further deduced that the BDSBAS adopted a method with the resolving of the orbit and clock error separated. It was a valid method to reduce the resolving dimension. www.nature.com/scientificreports/ Considering that the BDS GEO satellites did not provide ranging service, the accuracy exponent was set as a fixed value of "15" which indicated that the satellite ranging signal should not be used.
Broadcasted strategy of the BDSBAS-B1C. Up to now, BDSBAS has not published the broadcasted strategy of the BDSBAS-B1C message, so does WAAS and EGNOS. Though the RTCA DO-229E 12 has constrains the maximum update interval of each type, each SBAS has adopted different broadcasting strategies. Compared with WASS and EGNOS, the update interval of BDSBAS-B1C message was rather fixed. The update interval of the BDSBAS augmentation message was shown in Table 3 and Fig. 7.
Through the analysis of the message types broadcasted on Dec 11, 2020 (Fig. 5), it could deduced that the specific broadcasting strategy was as follows: Table 2. Fast correction, positioning and clock correction information of GPS satellites broadcasted from Dec 11 to 31, 2020.

Fast correction and integrity information (only available)
Position correction www.nature.com/scientificreports/  In the formula, t MT2 , t MT3 and t MT4 referred to the broadcasted time of the MT2-4; t 0 [6] [6] referred to the time of day t 0 modulo 6 s.

Clock correction (s) Fast correction (m) UDREI X (m) Y (m) Z (m)
(2) The update interval of the MT1, MT7, M9, M10 and M17 was 120 s, and the update cycle could be described as the formula (5).
In the formula, t MT1 , t MT7 , t MT9 , t MT10 and t MT17 referred to the broadcasted time of the MT1, MT7, MT9, MT10 and MT17; t 0 [120] referred to the time of day t 0 modulo 120 s.
(3) The update interval of the MT18 and MT26 was 240 s, and the update cycle could be described as the formula (6).    www.nature.com/scientificreports/ (4) The update interval of the MT25 and M28 was 120 s, and the number of broadcast groups in each update cycle was relative to the visibility and availability of the satellites. (5) When there was no valid information generated, the MT0 or MT63 would be broadcast.

Evaluation of the message performance
As BDSBAS is still in testing stage, the service boundary has not been published. Assuming the service area of the BDSBAS SF service was within China, some testing terminals were set in the central and boundary areas of China to test the accuracy of the UERE and the SF PE with the different correction parameters in BDSBAS-B1C message.

UERE evaluation with/without the support of the BDSBAS-B1C message. The pseudorange
residual error was the difference between the raw pseudorange and the reference range. The reference range could be gain with the true range between the corrected satellite position and the receiver, all the broadcasted corrections, tropospheric delay, receiver clock bias, and multipath. Therefore, the UERE mainly comprised the error in the space segment and the pseudorange residual error in the ground segment. It could be calculated as the formula (8).
In the formula, ρ ′ refers to the observed pseudorange; ρ refers to the geometrical distance between the receiver and the satellite. The points of the receiver should be measured by the professional surveying team and used for the precise orbit determination; c refers to the velocity of light; δt r refers to the clock error of the receiver; δt s refers to the clock error of the satellite; d tro refers to the tropospheric delay; d rel refers to the delay caused by the relativistic effect; d mul refers to the multipath delay; d orb refers to the orbit error calculated by the orbit correction parameters; d clk refers to the clock error calculated by the clock correction parameters; d fast refers to the error calculated by the fast correction parameters; d grid refers to the error calculated by the ionospheric correction parameters of the IGPs; ε p refers to the residual error. We use the value of the 95% percentile UERE, a 95% quantile statistics, as the evaluation accuracy of the day.
As to UERE of the GPS standard positioning service (SPS), the evaluation equation can be described as the formula (9).
In the formula, d ion refers to the error calculated by the ionospheric model parameters which are broadcasted in the navigation message.
It could be seen that the difference between the UERE SBAS and the UERE SPS was not only in the augmentation parameters used, but also in the correction mode of the ionospheric error.
To analyze the UERE of the GPS satellites in different correction modes, four groups of experiments were carried out with the observation data obtained by the known point in Beijing, Sanya, Chengdu, Shantou, Harbin and Urumchi from Dec 11 to 31, 2020. The four specific scenes were constructed as follows: (1) Tables 4, 5 and Fig. 8. www.nature.com/scientificreports/ It could be seen that: (1) Compared with the accuracy of the GPS SPS UERE in the specified area, BDSBAS could effectively improve the accuracy when all or part of the correction parameters applied. (2) The accuracy could not be obviously improved with only the position and clock corrections or the ionospheric corrections applied. (3) As the satellite came in and out the service boundary, the variation range of the UERE SBAS is more gentle than the UERE SPS . The variation scope of the scene 1 and scene 3 was quiet similar. It could be seen that the two kind of ionospheric correction mode did not have significant difference.

Evaluation of the SF PE with/without the support of the BDSBAS-B1C message
To analyze the SF PE of the GPS satellites with BDSBAS support, four groups of experiments were carried out with the observation data and navigation message obtained from the known points in different service areas from Dec 11 to 31, 2020. The four constructed scenes were the same as the scenes mentioned above. The horizontal positioning error (HPE), vertical positioning error (VPE) and the corresponding PDOP were given in Table 6, Figs. 9, 10, 11 and 12. It could be seen that: www.nature.com/scientificreports/ www.nature.com/scientificreports/ www.nature.com/scientificreports/ (1) Compared with the single point PE of the GPS SPS obtained by the navigation message broadcasted by the GPS satellites, BDSBAS could effectively improve the positioning accuracy with all the correction parameters applied. Whereas, the accuracy could be hardly improved when only the position and clock corrections or the ionospheric corrections were applied. (2) Through the comparison of the different scenes, it could be seen that the positioning accuracy in the vertical direction has more improvements than the accuracy in the horizontal direction. It may benefit from the effective correction of the ionosphere in the vertical direction. (3) The PDOP indicated the availability of the correction parameters for the visible satellite. For the regions with high availability of the ionospheric corrections, such as Beijing and Chengdu, the PDOP was almost the same in different scenes and the PE was mainly affected by the accuracy of the correction parameters. For the boundary area of the BDSBAS service, such as Harbin, there was obvious difference in different scenes. The reason for the lower PDOP in scene2 and scene3 was probably that the ionospheric corrections were applied in scene2 and scene3 and the availability of the ionospheric corrections was low. www.nature.com/scientificreports/

Summary
Currently, BDSBAS has realized the broadcasting of the augmentation message with three GEO satellites and constructed along with other BDS-3 services. The conditions for initial operation have been met. Though the above analysis, the basic conclusion could be gain as follows: (1) The construction and content of the augmentation message broadcasted in the BDSBAS-B1C signal has basically met the requirement of the RTCA DO-229E. Whereas, the offset parameters of BDSBAS SNT and UTC and the SBAS service message have not been broadcasted. (2) BDSBAS has specified a broadcasting strategy of the BDSBAS-B1C message with reference to the standards published by the ICAO, RTCA and other international organizations. Whereas, the fixed timing sequence may be more suitable for the case of no alarm events as the message containing the alert condition should be broadcasted four times in four seconds and relace the fixed message. It should be further verified if it is suitable in the case of alarm. (3) In contrast to the accuracy of the UERE and single point PE obtained by the navigation message of the GPS satellites in the specified area, the BDSBAS could effectively improve the monitoring results. The results showed that the accuracy and availability of the ionospheric parameters was one of the most important factors. To satisfy the requirements of Category I precision approach (CAT-I) as WAAS and EGNOS, more effort should be put into to improve the availability of the ionospheric corrections in the boundary areas. www.nature.com/scientificreports/

Data availability
The data was provided by the BDSBAS civil service platform and the international GNSS Monitoring and Assessment System (iGMAS).